1. Field of the Invention
The present invention relates to a method for analyzing spectra including contributions from scattering so-called inverse scattering analysis using a renormalized form of the Lippmann-Schwinger equations, and to a system implemented on a computer and attached to an analytical instrument where a spectrum of interest is received by the instrument and analyzed in the computer using the renormalized form of the Lippman-Schwinger equations of this invention.
More particularly, the present invention relates to a method for analyzing spectra including contributions from scattering so-called inverse scattering analysis using a renormalized form of the Lippmann-Schwinger equations, where the renormalized equation permits absolute and uniform convergence of the equation regardless of the strength of interaction in the system from which the spectrum was obtained, and to a system implemented on a computer and attached to an analytical instrument where a spectrum of interest is received by the instrument and analyzed in the computer using the renormalized form of the Lippman-Schwinger equations of this invention.
2. Description of the Related Art
Many spectral characterization include inverse scattering components resulting from internal reflections of an incident waveform. These inverse scattering components can give information on both near field and far field properties of the object being analyzed. However, traditional application of the Lippmann-Schwinger equations to analyzed spectra including inverse scattering components are less the satisfactory because the Lippmann-Schwinger equations often do not converge or give oscillatory solutions that must be truncated to product approximate and sometimes misleading analyses.
Thus, there is a need in the art for an improved mathematical theory for analyzing inverse scattering components that always permits solutions because the equations absolutely and uniformly converge.